To answer your question directly: both
at are viable options for setting someone's location.
at would imply a very very close proximity to the bar (think, able to touch it)
by would imply proximity, but could just be the general vicinity of it
In this particular case, I would choose
at since it's likely that they're physically quite close if they're talking to the bartender (barring yelling from several feet back).
However, there are a couple other things with your phrasing that bother me. I would likely word it:
When both of you are standing at the bar ordering a drink, and a bartender asks you to pay now or open a tab.
- your use of the "you're" contraction seems alien here. I think it's because
you isn't the subject, but rather the object of the preposition
- the verb
stand should be
- I believe
asks to pay now is incorrect (at the least, it sounds very odd). You could say
asks if you want to pay now or
asks you to pay now.